Could life develop in a galaxy with a quasar at its centre?

Quasars are a type of Active Galactic Nucleus that inhabit the centres of some galaxies. They are among the most energetic objects known in the universe, emitting up to a thousand times the energy output of the Milky Way in radiation across the electromagnetic spectrum from X-rays to the far infrared with some quasars also being strong sources of radio emissions and of gamma-rays.

Quasars are powered by accretion of material into supermassive black holes in the centre of galaxies. It is thought that most galaxies, including the Milky Way, have gone through an active stage, appearing as a quasar or some other class of active galaxy, and are now quiescent because they lack a supply of matter to feed into their central black holes to generate radiation.

Does this mean that the amount of radiation on a planet in a quasar galaxy would prevent the development of the carbon-based life similar to what we have on Earth?

There is some evidence that the Milky Way black hole has been active in the relatively recent past. Joss Bland-Hawthorn (et.al) describe large-scale ionization cones in the Galaxy that they say indicate a "Seyfert explosion ($$10^{56}-10^{57}$$ erg) that occurred in the Galactic Centre a few million years ago."